Question

# A retailer buys a cooler for Rs. 1200. His overhead expenses are Rs. 40. If he sells the radio for Rs. 1550, then determine his profit(in percent).

Hint: We will use the formula, gain= S.P -C.P, where the SP is given as Rs. 1550 and the total cost price will be (Rs. 1200+Rs. 40). Then, we will use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ by substituting the values in it, to get the gain percentage.

We have the cost at which the cooler was purchased by the retailer = Rs. 1200
The overhead expenses that were taken up by the retailer = Rs. 40
The amount for which the cooler was sold by the retailer = Rs. 1550
Hence the gain earned by the retailer = Rs 1550-Rs (1200+40) = Rs. (1550-1240) =Rs. 310
(Because the overhead charges are also taken up by the retailer, so, they also go into the cost price)
Hence the gain earned by the retailer is equal to Rs.310
Gain percentage is defined as the amount of gain earned per 100 units of cost price.
We have, the gain on Rs 310 of C.P = Rs. 1240
Hence, we have
The gain on Re. 1 of C.P $=\dfrac{310}{1240}=\dfrac{1}{4}$
Hence gain per Rs. 100 of C.P $=\dfrac{1}{4}\times 100=25\%$

Hence the gain percentage of the retailer = 25%

Note: We can directly calculate gain using the formula,
$gain\%=\dfrac{gain}{C.P}\times 100$
Substituting the values of gain and C.P, we get,
$gain\%=\dfrac{310}{1240}\times 100=25\%$
Also, the students must remember to add Rs. 40 to Rs. 1200 to get the total cost price, else it will lead to error in the final answer.